In some plants, the pistils don't form until a few days after the stamens do. How would this keep a plant from self-pollinating?

Pollination is the process in which pollens are transferred to the female reproductive organs of the plant, where fertilization will take place and give birth to more new plants.

Some plants have the ability to make the stamens mature first before the pistils to prevent itself from self-pollinating. This is because factors found within the environment such as animals, wind, among other, may pre-maturely disperse the pollen into the stigma of the plant. If a situation as such would happen, there will be no pollen left in that flower to land on the stigma to start the fertilization of the plant.